Semiparametric regression of multivariate panel count data with informative observation times

Multivariate panel count data occur in many fields such as medical and social science studies in which several outcomes of interest are measured simultaneously and repeatedly over time. When the observation times are not pre-specified, it is very likely that either the observation or follow-up times are informative about the response process. In such situations, most existing approaches either specify a dependence structure with some fixed distributions or assume independence given some covariates, which may not be true and result in misleading conclusions. In this paper, we present a joint modeling approach that allows the possible mutual correlations to be characterized by time-dependent random effects. Estimating equations are developed for the parameter estimation and the resulted estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed estimators is assessed through a simulation study and an illustrative example from a maternal influenza immunization study on infant growth is provided.